〜べくもない

Meaning

Indicates that, by natural reason, there is no way one could possibly do so. An archaic expression stating strong impossibility, that there was no chance of realization from the start.

Examples

素人の私に、専門家の判断の是非など分かるべくもない。 As an amateur, I have no way of judging whether the expert's decision is right.
これほど差がついては、もはや逆転など望むべくもない。 With such a wide gap, there is no longer any hope of a comeback.